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Theorem bj-nfs1t2 31275
Description: A theorem close to a closed form of nfs1 2161. (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
bj-nfs1t2  |-  ( A. x F/ y ph  ->  F/ x [ y  /  x ] ph )

Proof of Theorem bj-nfs1t2
StepHypRef Expression
1 nfr 1928 . . 3  |-  ( F/ y ph  ->  ( ph  ->  A. y ph )
)
21alimi 1678 . 2  |-  ( A. x F/ y ph  ->  A. x ( ph  ->  A. y ph ) )
3 bj-nfs1t 31274 . 2  |-  ( A. x ( ph  ->  A. y ph )  ->  F/ x [ y  /  x ] ph )
42, 3syl 17 1  |-  ( A. x F/ y ph  ->  F/ x [ y  /  x ] ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1435   F/wnf 1661   [wsb 1790
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-12 1909  ax-13 2057
This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1658  df-nf 1662  df-sb 1791
This theorem is referenced by:  bj-nfs1  31276
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